Question

What the is the polar form of `y = 1/y-xy+x^2/y`?

Answer 1

`rsin(theta)=1/(rsin(theta))-r^2sin(theta)cos(theta)+(rcos^2(theta))/(sin(theta))`

Simplified: `r^2(cos(theta)-cos(3theta))-4=(2r)^2cos(2theta)`

Explanation:

`x=rcos(theta), y=rsin(theta)`

Substitute and Simplify

`rsin(theta)=1/(rsin(theta))-r^2sin(theta)cos(theta)+(rcos^2(theta))/sin(theta)`

Alternate: `r^2sin(theta)=csc(theta)-r^3sin(theta)cos(theta)+r^2cot(theta)cos(theta)`